There is some evidence that the
the proto-Earth collided with another planetesimal, perhaps
the size of Mars. Some of the material blasted
outwards in the collision clumped together under its
own gravity to form a body in orbit around the remaining
proto-Earth -- a body we call the Moon.

But -- what if we were wave our magic wands
and prevent any such moon-producing collision?
What if the Earth had formed all by itself,
without a Moon?
How would the subsequent evolution of the Earth,
and life upon it, been changed?

I will consider a number of consequences,
starting with very definite and uncontroversial
ones, then working my through to some which are
more speculative.
As you will see, there was been a great deal of
thought and discussion of these ideas by
many people over the past century;
I am merely collecting them.

When the Apollo astronauts and the Russian Lunakhod
rovers visited the Moon,
they left behind several special "retroreflectors":
sets of cubical mirrors which are designed
to reflect light directly back in the direction
whence it came.

Several observatories on Earth,
such as the McDonald Observatory in Texas

shine pulses of light from powerful lasers at these
retroreflectors,
then look carefully for the (very few) returning
photons.
The time it takes for light to make the round
trip provides scientists with a precise
measure of the distance between the Earth and Moon.
With care, the distance can be measured VERY precisely.
The table below shows the error budget for the
measurement of a single photon;
typical experiments detect tens or hundreds of
photons.

Over the past few decades, lunar-ranging measurements
have shown that the semi-major axis of the Moon's
orbit is slowly increasing, by
3.82 +/- 0.07 cm/year
(Dickey et al., Science 265, 482 (1994)).
Why should that be happening -- and what effect
might that have on the Earth?

The answer involves tides.
Tides are bulges one body caused by the gravitational
pull of an external body;
or, more precisely, caused by the DIFFERENCES
in the gravitational pull of an external body.
Consider the Earth, its oceans, and the Moon.

The strength of the gravitational force decreases
as the square of the distance between two objects.
So the Moon pulls just a bit harder on the near side
of the ocean than it does the center of the Earth ...
and just a bit harder on the center of the Earth
than on the far side of the ocean.

These slight differences
in gravitational forces pull a blob of water outwards
away from the Earth on side nearest the Moon;
and they pull the Earth away from the blob of water
which is on side farthest from the Moon.
The net result is to deform the
oceans into a somewhat oval shape.

Now, if we were to hold the Earth and Moon fixed in place
(with some very strong pieces of string, perhaps),
then that would be the end of the story:
a stationary tidal bulge would point towards
the Moon.
People on vacation might travel to the portions
of the world under the bulge to swim in a very
slightly deeper ocean.

However, the Earth and Moon are not fixed in
place.
They are instead dancing together in a three-part manner:

the Earth is rotating around its own axis
(once about every 23 hours and 56 minutes)

the Moon is rotating around its own axis
(once about every 27.3 days)

the Moon is revolving around the Earth
(once about every 27.3 days)

Because the Earth rotates so quickly,
friction between the ocean floor and the water
drags the tidal bulges forward a bit,
so that they "lead" the Moon slightly.

Let's simplify things, since it will make the diagrams
to come easier to understand.
We'll put a dot in each of the tidal bulges,
and pretend that all the mass of the water in each bulge
is concentrated at that point.

The water in each of the ocean bulges exerts a
gravitational force on the Moon.
The near-side bulge pulls the Moon in a direction
which is slightly tilted in the direction of the Moon's
orbital motion,
while the far-side bulge pulls the Moon very slightly
backwards, opposite to its orbital motion.
But because the near-side bulge is closer,
its pull is a bit stronger.
The total force from the ocean water has
a small component which pulls the Moon
forward along its orbit,
speeding it up very slightly.

Because the net tidal force pulls the Moon forward
in its orbit, it increases the Moon's orbital speed;
that increase in speed causes the Moon to shoot
ahead a little faster and overshoot its
circular orbit.
It ends up a bit farther from the Earth,
in a slightly larger orbit.

In its new, larger, orbit,
the Moon takes LONGER to complete one revolution
around the Earth;
this may seem a bit counterintuitive,
since it was a component of gravitational
force forwards along its orbit that started
the whole process,
but the increase in gravitational potential
energy as the Moon recedes from the Earth
leads to a decrease in kinetic energy.

Okay, so the Moon recedes from the Earth --
but what about the Earth?
Does anything happen to IT due to these
tidal interactions?
Yes, indeed.
Look again at the misaligned tidal bulge of the oceans:

Over the course of the next 18 hours, the Earth rotates
over three-quarters of a full circle, but the
Moon moves through only a tiny fraction of its orbital circle.
Since the tidal bulges track the Moon, they, too,
stay nearly in place.

The Earth rotates UNDERNEATH the tidal bulges,
moving much more quickly than they do.
The friction between the solid body of the Earth
and the waters of the ocean acts to
slow down the Earth's rotation
(this is quite a simplification -- read
this paper on tides and friction for more details).
So the Earth's period of rotation grows just
a little bit longer ... very slowly.

To sum it up,

the Moon moves outwards, away from the Earth

the Earth's period of rotation increases

If you wish, you may use the conservation of angular momentum
to determine how these two changes are connected.
The total angular momentum of the Earth-Moon system
remains the same: the Earth's spin angular momentum
decreases as the Moon's orbital momentum increases.

Our measurements of the increase in the Moon's orbital
radius (about 3.8 cm each year) can be turned
around to yield the rate at which the Earth's rate of
rotation is decreasing.
That turns out to be about 2.3 milliseconds added to a day,
over the course of a century.

At the present time,
the small overall increase in the length of a day
doesn't seem very important.
Very few people pay much attention to the occasional
leap seconds which are inserted into the official
time systems.
Over the course of an entire human life,
days grow longer, on average, by about
the duration of one flap of a honeybee's wings.

But if one is patient enough,
this very slow rate can add up to quite a
large change.
For example, a perfect clock
which was started from "12:00:00" in the year 1000 BCE
when the Sun was directly overhead,
would at the present time show the Sun
to be overhead about half an hour after 12:00:00.
The Earth, in other words,
should have "lost half an hour" over the past millenium.

Well, that's the theory, anyway.
Is there any evidence for it?

Yes!

We have records of eclipses which took place thousands
of years ago.
This bit of cunieform, for example,

is a Chinese record of a lunar eclipse of September 4/5, 434 CE.
Without the slowing of the Earth's rotation,
these eclipses could not have been seen at the locations
and times described in the records;
the eclipse paths would have been shifted by hundreds or thousands
of miles.

Another sort of evidence comes from fossils of
marine creatures and algae.
Some well-preserved specimens show regular patterns
of striations or lines which occur in
groups.
Similar patterns in living creatures can be caused
by material deposited on a cycle of length one
month, influenced by the change in ebb and neap tides
(cycles of other lengths also occur).
If we interpret some of the fossil patterns
to indicate monthly changes, and others to represent
annual changes, we can figure out how many months
occur over the course of a year.
Since the length of the year has certainly not
changed appreciably over geologic time,
we can attribute changes in these patterns
to a change in the length of the month
over times in the geologic record.

Over the course of millions of years, the change in
the length of the Earth's rotation amounts to many hours.
The earliest evidence mentioned in Pannella's paper
dates from about 1.8 billion years ago,
and suggests that there were about 450 days in the year
at that time.
That means that each day was only about 20 hours long.
Extrapolating to earlier times is difficult,
since there are interactions between the
locations of the continents, the shape of the oceans,
and the efficiency of tidal friction.
Nonetheless, it is possible that the very
young Earth may have had a rotation period of
less than 10 hours.

Okay, that was a long introduction, but,
now that we know what sort of influence
the Moon has had on the Earth,
we can
finally start to answer the question
"What would the Earth be like
if it didn't have a Moon?"

For one thing, it would probably
be rotating more rapidly.
The Sun, it is true, does
cause tides of its own in the Earth's oceans,
but its tidal effects are weaker than
those of the Moon.
If the initial rotation period of the Earth
was, say, 6 hours, then without a Moon,
it might have slowed due to solar tides
to only, say, 10 hours.
What consequences might follow from such a
fast rotation?

Perhaps the Earth's atmosphere might show
some differences.

The day/night cycle of cooling and heating would
run more rapidly. Would that give thunderstorms
enough time to build up over the course of a day?

The other major planets in the solar system which
rotate in only 10 hours are the gas giants:

Their atmospheres -- while very, very much thicker
than the Earth's, and composed of materials under
much colder conditions -- exhibit belts and zones;
would the Earth's atmosphere behave in a similar
manner if our planet rotated more quickly?

The planet most like our Earth in many ways is Venus;
but Venus has a much thicker (and nastier) atmosphere.

Venus with (left) and without (right)
its atmospheric blanket

It has been postulated in the past by some that the Moon might
be somehow responsible for the lack of a similarly
thick atmosphere around the Earth.
I do not understand the mechanism by which the Moon
would remove most of the atmosphere, or prevent its
generation via outgassing, so I give this idea
little weight. It certainly is a Good Thing
that our Earth does not have a Venus-like atmosphere,
with its immense pressure (90 atm at the surface)
and strong greenhouse effect (leading to temperatures
over 700 Celsius).

As mentioned earlier, without the Moon,
tides would be weaker than they currently are.
Instead of advancing and retreating across
the sands by tens of meters,
the ocean waters might only oscillate
by a few meters.
That, in turn, would create many fewer
tidal pools.

Some people believe that tidal pools,
with their combination of shallow, still
water, plenty of sunlight, and regular influx
of fresh materials, plus evaporation
to concentrate the brew,
might have provided the environment
in which some of the first forms of life
on Earth might have developed.
With fewer tidal pools,
would the earliest, simplest self-replicating
molecules have formed in just one or two billion years?

Recent work on the formation of life on Earth
has moved in a different direction, actually.
The current "favorite" location for the
formation of the earliest life
is somewhere deep in the oceans,
near a hydrothermal vent.

If this is true, then the lack of a Moon
would not have discouraged the earliest
forms of life on Earth.